An important module in our fabrication sequence optimization framework is to predict the distortion of the fabricated component. The modelling and simulation of additive manufacturing processes is itself an active research field [1]}, [2]}, [3]}, [4]}. A multitude of process models have been proposed, with different levels of accuracy and computational complexity. WAAM involves time-dependent thermal and mechanical states along with the successive addition of melted material. This could be modelled by a fully coupled transient thermo-mechanical finite analysis. Such modelling allows to gain insights into the development of residual stresses and distortion due to the fabrication sequence as well as deposition rates and heat sink characteristics [5]}, [6]}, [7]}, [8]}. Similar to multi-pass welding simulation, WAAM simulation involves two major steps: a thermal analysis where the temperature distribution caused by a moving heat source is determined, and a structural analysis which accounts for a series of sequential load steps calculated in a transient thermal analysis [9]}. This coupled thermo-mechanical analysis however is computation intensive. It is prohibitive for numerical optimization of the fabrication sequence, since numerical optimization requires to simulate the fabrication process at each optimization iteration. An appealing alternative is the inherent strain method [10]}, [11]}, in which the residual stress and distortion are obtained by linear elastic analysis. Due to the computational advantages, inherent strain methods have been increasingly applied for modelling additive manufacturing processes [12]}, [13]}, [14]}, [15]}, [16]}. Inherent strain methods have been recently integrated in structural topology optimization for minimizing distortion. For instance, Allaire and Jakabčin [17]} proposed a level-set based topology optimization method that considers thermal residual stresses and thermal deformations during the layer-by-layer fabrication process. Pellens et al. [18]} incorporated an inherent strain method in density-based topology optimization to optimize support structures for limiting the vertical displacement of layers during fabrication. Also building upon density-based topology optimization, Misiun et al. [19]} integrated an inherent strain method to optimize the structural layout under distortion constraints. The inherent strain method has also been used in level-set based topology optimization for controlling distortion [20]}.
